7 citations · 38 across the 19 of their papers we have counts for
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Exponential iteration and Borel sets
David S. Lipham
We determine the exact Borel class of the points whose iterates under tend to infinity. We also prove that the sets of non-escaping Julia points for many of these funct…
A characterization of Erdős space factors
David S. Lipham
We prove that an almost zero-dimensional space is an Erdős space factor if and only if has a Sierpiński stratification of C-sets. We apply this characterization to spaces w…
Distinguishing endpoint sets from Erdős space
David S. Lipham
We prove that the set of all endpoints of the Julia set of which escape to infinity under iteration of is not homeomorphic to the rational Hilbert space $\math…
Erdős space in Julia sets
David S. Lipham
We prove that the rational Hilbert space , known as Erdős space, surfaces in complex dynamics via iteration of .
On cohesive almost zero-dimensional spaces
Jan J. Dijkstra, David S. Lipham
We investigate C-sets in almost zero-dimensional spaces, showing that closed C-sets are C-sets. As corollaries, we prove that every rim--compact almost zero-dimensional space…
The topological dimension of radial Julia sets
David S. Lipham
We prove that the meandering set for is homeomorphic to the space of irrational numbers whenever belongs to the Fatou set of . This extends recent results b…